Geodesic
A Note on Lawton's Theorem
Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 484-489

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DOI

We prove Lawton's conjecture about the upper bound on themeasure of the set on the unit circle on which a complex polynomial with a bounded number of coefficients takes small values. Namely, we prove that Lawton's bound holds for polynomials that are not necessarily monic. We also provide an analogous bound for polynomials in several variables. Finally, we investigate the dependence of the bound on the multiplicity of zeros for polynomials in one variable.
DOI : 10.4153/CMB-2016-066-x
Mots-clés : 11R09, 11R06, polynomial, Mahler measure 
Dobrowolski, Edward. A Note on Lawton's Theorem. Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 484-489. doi: 10.4153/CMB-2016-066-x
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     author = {Dobrowolski, Edward},
     title = {A {Note} on {Lawton's} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {484--489},
     year = {2017},
     volume = {60},
     number = {3},
     doi = {10.4153/CMB-2016-066-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-066-x/}
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